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Expected Value Problem Help

  1. Nov 2, 2012 #1
    1. A city has 74,806 registered automobiles. Each is required to display a bumper decal showing that the owner paid an annual wheel tax of $50. By law, new decals needed to be purchased during the month of the owner’s birthday. How much wheel tax revenue can the city expect to receive in November?



    2. expected value = E(X) = summation(x*f(x))
    Leibnitz's rule




    3. I thought there was not enough information in the problem. Can we assume that people are equally likely to be born in the different months of the year?
    Anyway, all I have is E(X) = (74,506*50)*1/12
    where the part in parenthesis is x and 1/12 is the probability function
    (not sure).
     
  2. jcsd
  3. Nov 3, 2012 #2

    Ibix

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    I think you are right that you need to assume a uniform distribution of birthdays, and I would write that assumption out explicitly.

    Just one question about your answer - what is the expected revenue in (say) February?
     
  4. Nov 3, 2012 #3
    Going by the same approach, it would be the same answer. Did you have something else in mind?
     
  5. Nov 3, 2012 #4

    Ibix

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    I think each day is equally likely...
     
  6. Nov 3, 2012 #5
    Ah, I see. So for November, E(X) = (74,506*50)*30/365
    and for February, assuming it's not a leap year, it would be E(X) = (74,506*50)*28/365

    Thanks for the help.
     
  7. Nov 4, 2012 #6

    Ibix

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    That is the right answer for a non-leap year - can you figure it out for an average year?
     
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